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The asymptotic nature of perturbative expansions in quantum field theory can arise from the factorial growth in the number of Feynman diagrams with loop order, as with instantons, or from a series of individual diagrams whose values grow…

With any max-stable random process $\eta$ on $\mathcal{X}=\mathbb{Z}^d$ or $\mathbb{R}^d$, we associate a random tessellation of the parameter space $\mathcal{X}$. The construction relies on the Poisson point process representation of the…

Using explicit methods, we provide an upper bound to the norm of the Busemann cocycle of a locally finite regular tree $X$, emphasizing the symmetries of the cocycle. The latter takes value into a submodule of square summable functions on…

We solve the growing asymmetric Ising model [Phys. Rev. E 89, 012105 (2014)] in the topologies of deterministic and stochastic (random) scale-free trees predicting its non-monotonous behavior for external fields smaller than the coupling…

We consider a model of the Riemann zeta function on the critical axis and study its maximum over intervals of length $(\log T)^{\theta}$, where $\theta$ is either fixed or tends to zero at a suitable rate. It is shown that the deterministic…

We present a new and efficient method for deriving finite-size effects in statistical physics models solvable by Bethe Ansatz. It is based on the study of the functional that maps a function to the sum of its evaluations over the Bethe…

We study the typical behavior of the harmonic measure in large critical Galton-Watson trees whose offspring distribution is in the domain of attraction of a stable distribution with index $\alpha\in (1,2]$. Let $\mu_n$ denote the hitting…

We study the behavior of high-dimensional robust regression estimators in the asymptotic regime where $p/n$ tends to a finite non-zero limit. More specifically, we study ridge-regularized estimators, i.e…

We consider an asymptotically stable multidimensional random walk $S(n)=(S_1(n),\ldots, S_d(n) )$. Let $\tau_x:=\min\{n>0: x_{1}+S_1(n)\le 0\}$ be the first time the random walk $S(n)$ leaves the upper half-space. We obtain the asymptotics…

For a subshift $(X, \sigma_X)$ and a subadditive sequence $\mathcal{F}=\{\log f_n\}_{n=1}^{\infty}$ on $X$, we study equivalent conditions for the existence of $h\in C(X)$ such that $\lim_{n\rightarrow\infty}(1/{n})\int \log f_n d \mu=\int…

We analyze the non-equilibrium dynamics of the O(N) Phi^4 model in the large N limit and for states of large energy density. The dynamics is dramatically different when the energy density is above the top of the tree level potential V_0…

We consider a null recurrent random walk $\mathbb{X}$ on a super-critical Galton Watson marked tree $\mathbb{T}$ in the (sub-)diffusive regime. We are interested in the asymptotic behaviour of the local time of its root at $n$, which is the…

The limiting extremal processes of the branching Brownian motion (BBM), the two-speed BBM, and the branching random walk are known to be randomly shifted decorated Poisson point processes (SDPPP). In the proofs of those results, the Laplace…

For every sufficiently well-behaved function $g:\mathbb{R}_{\ge 0}\rightarrow\mathbb{R}_{\ge 0}$ that grows at least linearly and at most exponentially we construct a tree $T$ of uniform volume growth $g$, that is, $$C_1\cdot g(r/4)\le…

For $\alpha \in (1,2]$, the $\alpha$-stable graph arises as the universal scaling limit of critical random graphs with i.i.d. degrees having a given $\alpha$-dependent power-law tail behavior. It consists of a sequence of compact measured…

We study the asymptotic number of certain monotonically labeled increasing trees arising from a generalized evolution process. The main difference between the presented model and the classical model of binary increasing trees is that the…

Place one active particle at the root of a graph and a Poisson-distributed number of dormant particles at the other vertices. Active particles perform simple random walk. Once the number of visits to a site reaches a random threshold, any…

A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a tree for every finite set of endpoints in…

Let $\mathcal{P}_{\lambda}:=\mathcal{P}_{\lambda\kappa}$ denote a Poisson point process of intensity $\lambda\kappa$ on $[0,1]^d,d\geq2$, with $\kappa$ a bounded density on $[0,1]^d$ and $\lambda\in(0,\infty)$. Given a closed subset…

We present a technique to study normalizing strategies when termination is asymptotic, that is, it appears as a limit, as opposite to reaching a normal form in a finite number of steps. Asymptotic termination occurs in several settings,…